WO2020090594A1

WO2020090594A1 - Hole processing tool, and design method, manufacturing method, and evaluation method for same

Info

Publication number: WO2020090594A1
Application number: PCT/JP2019/041590
Authority: WO
Inventors: 健一郎松崎; 孝宏劉; 恵三塚本
Original assignee: 株式会社アヤボ; 国立大学法人鹿児島大学; 国立大学法人大分大学
Priority date: 2018-10-31
Filing date: 2019-10-24
Publication date: 2020-05-07
Also published as: EP3875200A4; JPWO2020090594A1; CN112996622A; EP3875200A1

Abstract

Provided is a method for simply evaluating a simulation result on the basis of the Matsuzaki-Liu model. This hole processing tool for forming a hole is provided with a plurality of cutting edges, wherein when the cutting edges are applied to the Matsuzaki-Liu characteristic equation, the maximum real part Tσ_MAX is in the range of a predetermined threshold with respect to the maximum real part Rσ_MAXX of a reference hole processing tool if N_o is the integer value closest to the imaginary part of a quasi-static characteristic root s, which is a characteristic root at the vibration frequency ω=0, and if the maximum real part σ_MAX is the maximum real part of the quasi-static characteristic root s that satisfies 3≤N_o≤2n+1 (n is the number of cutting edges).

Description

Hole processing tool and its designing method, manufacturing method and evaluation method

The present invention relates to a hole drilling tool and its designing method, manufacturing method, and evaluation method. This hole drilling tool is suitably used, for example, for reaming. Similarly, it is preferably used for general drilling such as end milling and drilling.

For example, in reaming, polygonalization of a machined hole is one of the causes for lowering the hole machining accuracy. Non-Patent Document 1 proposes a solution to this problem.
In this non-patent document 1, the mechanism of the machined hole polygonalization phenomenon in reaming is considered to be a self-excited vibration phenomenon due to a time delay. A characteristic equation based on the so-called Matsuzaki-Liu model has been proposed. Based on the characteristic roots, we are simulating the placement of cutting edges that can suppress self-excited vibration in a reamer (hole drilling tool).
A proof test was conducted on a reamer that was evaluated to be able to suppress self-excited vibration in such a simulation, and hole drilling with high roundness was realized.

In the simulation described in Non-Patent Document 1, the angle sequence of the cutting edge of the reamer to be evaluated is substituted into the characteristic equation of the Matsuzaki-Liu model, and this is analyzed to form a digonal to 13-gonal hole. As a matter, the chart is made by correlating the frequency and its characteristic root for each polygon. Then, the obtained chart is judged to judge whether or not the angle distribution of the cutting edge to be evaluated is good. Please refer to FIG. 4 and FIG. 5 as examples of the chart shown in Non-Patent Document 1.
More specifically, the maximum value (real part) of the characteristic roots of the dihedral to 13-diagonal chart obtained as a result of the simulation is observed. Then, it is considered that the influence of the polygon having the maximum value of the characteristic root exceeding zero appears during the reaming process. The larger the value of the characteristic root, the stronger the effect. Therefore, all the charts for the triangles to the triangles are observed all over, and the range of the angles of the cutting edges at which the value of each characteristic root is equal to or less than zero or close to zero is determined as a good product.
In other words, the above-mentioned evaluation work has to be carried out one by one for the arrangement of the angles of the cutting edges to be evaluated, which is troublesome.

Therefore, the present inventors have studied a method for simply evaluating the results of the simulation based on the Matsuzaki-Liu model.
As a result, I noticed that the curves in the charts shown in FIGS. 4 and 5 are all gentle. Therefore, it was considered that the value when the frequency ω was zero (the value on the vertical axis in the chart) reflected the maximum value. Note that if the frequency ω is set to zero, the characteristic equation of the Matsuzaki-Liu model is simplified (the term including ω can be ignored), and the calculation speed is also improved.

In this way, the characteristic root when the frequency ω = 0 is named as a quasi-static characteristic root.
This quasi-static characteristic root is specified by calculation for all polygons, and the quality of the angle distribution of the cutting edge to be evaluated is evaluated by the maximum value among them.
However, in order to judge the quality based only on the numerical value (the characteristic root at the frequency ω = 0) obtained by the calculation, the judge is required to have the skill.
In addition, it is difficult to objectively grasp the degree of quality.

Therefore, the inventors have examined what is a standard for evaluating the value of the quasi-static characteristic root. As a result of the study, the maximum value σ _MAX (maximum real part) of the real part in the quasi-static characteristic root was focused. Then, with reference to the maximum real part Rσ _MAX of the cutting edges arranged at a certain angle, this is compared with the maximum real part Rσ _MAX of the angle of the cutting edge to be evaluated.
In particular, when based on the those regular intervals a sequence of angle of the cutting edge, a strong correlation appears between the difference between the maximum real part Tishiguma _MAX evaluated and its maximum real part Arushiguma _MAX test results Found. Here, the test result indicates the roundness when the actual reamer processing is executed by the reamer provided with the angular distribution of the cutting edges to be evaluated.

In the example, a reamer (6 blades) is taken as an example, and the maximum real part R σ _MAX of the quasi-static characteristic root is used as a reference hole processing tool by using cutting edges that are evenly spaced, using the characteristic equation of the Matsuzaki-Liu model. I calculated. Further, the maximum real part T σ _MAX of the quasi-static characteristic root of the object to be evaluated (those having various angles of cutting edges) was similarly calculated. Then, the difference between them (maximum real part T σ _MAX −maximum real part R σ _MAX ) was calculated. The difference is referred to as a QCR value (QCR: Quasi-static characteristic root).
On the other hand, reaming was performed on the reference hole processing tool and the evaluation target hole processing tool, and the roundness of the obtained hole was measured.
The relationship between the measured roundness and the QCR value described above is shown in FIG.
From the result of FIG. 8, it can be seen that there is a high correlation between the QCR value and the roundness.

Based on the above findings, the first aspect of the present invention is defined as follows. That is,
A hole processing tool for forming a hole having a plurality of cutting edges,
When each cutting edge is applied to the characteristic equation of the Matsuzaki-Liu model, the integer value closest to the imaginary part of the quasi-static characteristic root s, which is the characteristic root at the frequency ω = 0, is N ₀ , and 3 ≦ N ₀ ≦ 2n When the maximum real part of the quasi-static characteristic root s that satisfies +1 (n is the number of cutting edges) is the maximum real part σ _MAX ,
Its maximum real part Tishiguma _MAX the maximum real part Arushiguma _MAX of the reference drilling tool is within the predetermined threshold, the drilling tool.
In the hole drilling tool of the first aspect defined in this way, since the maximum real part Tσ _MAX of the reference hole drilling tool is within the range of the predetermined threshold value with respect to the maximum real part Rσ _MAX of the reference hole drilling tool, from the relationship of FIG. As you can see, it enables drilling with high roundness.
Further, according to the hole drilling tool of the first aspect thus defined, the maximum real part is evaluated in comparison with the reference hole drilling tool, so that the evaluation is objective.

The second aspect of the present invention is defined as follows. That is,
A hole drilling tool stipulated in the first aspect, wherein the quasi-static characteristic roots in the characteristic equation correspond to 2 to 13 polygons,
The reference hole processing tool is one in which the cutting edges are arranged at an equal pitch,
The absolute value of the difference between the maximum real part Tσ _MAX of the target hole drilling tool and the maximum real part Rσ _MAX of the reference hole drilling tool is 0.075 or more. However, Tσ _MAX ≤ Rσ _MAX

The hole drilling tool of the second aspect defined in this way reflects the result of FIG. 8 more specifically, and if a hole drilling tool having such characteristics is used, the hole to be drilled is expensive. Roundness can be secured.
The reason why the quasi-static characteristic root is limited to the 13-sided polygon or less is that the shape exceeding the 13-sided polygon can be said to be close to a circle, so that even if this occurs, it does not significantly affect the actual drilling. .. On the other hand, when 14 or more corners are reflected, if the maximum real part of the quasi-static characteristic root obtained there becomes large, there is a possibility that it will be a large value as the QCR value, although it has little effect on actual hole drilling. There is.

The third aspect of the present invention is defined as follows. That is,
In the hole drilling tool defined in the second aspect, the absolute value of the difference between the maximum real part Tσ _MAX of the target hole drilling tool and the maximum real part Rσ _MAX of the reference hole drilling tool is 0.10.
The hole drilling tool defined in the third aspect as described above more specifically reflects the result of FIG. 8. If a hole drilling tool having such characteristics is used, a hole to be drilled is formed. Therefore, a high roundness can be secured.

The fourth aspect of the present invention is defined as follows. That is,
In the hole drilling tool defined in the second aspect, the absolute value of the difference between the maximum real part Tσ _MAX of the target hole drilling tool and the maximum real part Rσ _MAX of the reference hole drilling tool is 0.125 or more.
The hole drilling tool of the fourth aspect thus defined further reflects the result of FIG. 8, and if the hole drilling tool having such characteristics is used, a higher roundness can be obtained in the hole to be drilled. The degree can be secured.

The fifth aspect of the present invention is defined as follows. That is,
In the second to fourth specified hole drilling tools, the cutting edge number n is 6.
The hole drilling tool of the fifth aspect thus defined further reflects the result of FIG. 8, and if the hole drilling tool having such characteristics is used, the hole drilling tool having a higher hole Roundness can be secured.

The sixth aspect of the present invention is defined as follows. That is, in the hole drilling tool defined in the second to fifth aspects, when the dividing angle αi between the cutting edge i and the cutting edge i + 1 adjacent thereto in the counter-rotational direction is viewed all around the hole drilling tool. The size relationship and the size relationship when the margin width tmi + 1 of the cutting edge i + 1 and / or the land width ti + 1 are viewed in the entire circumferential direction of the hole drilling tool are the same.

According to the hole drilling tool defined in the sixth aspect defined in this way, the width (margin width, land width) of the portion of the cutting edge that is in contact with the work material is changed. The change corresponds to the size of the angle (division angle) of the adjacent cutting edges. That is, the larger the division angle, the greater the load on the portion of the cutting edge on the downstream side in the rotation direction that contacts the work material. Therefore, the wear of the portion is likely to progress. Therefore, if the division angle is increased, the width of the cutting edge portion in contact with the work material is correspondingly increased to suppress the progress of wear and prevent uneven distribution of wear.

The seventh aspect of the present invention is defined as follows. That is, in the hole drilling tool defined in the sixth aspect, a ratio (α1: α2: ...: αn) of the split angle when the split angle αi is viewed over the entire circumference of the drill and the margin width are the tool. The margin width ratio (tm2: tm3: ...: tmn: tm1) when viewed over the entire circumference and / or the land width ratio (t2: t3: ...) when the land width is viewed over the entire circumference of the processing tool. ...: tn: t1) match.
According to the hole drilling tool of the seventh aspect defined in this way, the division angle and the width (margin width, land width) of the cutting edge portion in contact with the work material are proportional to each other, so that uneven wear occurs. Will be even less.

The eighth aspect of the present invention is defined as follows. That is,
In the hole drilling tool defined in the sixth or seventh aspect, the margin portion of the cutting edge is covered with a hard film.
According to the hole drilling tool of the eighth aspect defined in this way, uneven distribution of wear can be prevented while reducing the use of the hard coating material.
The hole drilling tool described above is suitably used for reaming (the ninth aspect).

FIG. 1 is a drawing-substituting photograph showing a reamer that is an example of the hole drilling tool of the present invention. FIG. 2 is a schematic diagram showing the basic parameters of the Matsuzaki-Liu model applied to a 6-hole cutting tool. FIG. 3 is a schematic diagram showing the analysis principle of the Matsuzaki-Liu model. FIG. 4 shows the analysis results of the hole making tool provided with equally-spaced cutting edges. The horizontal axis of each chart shows the frequency and the vertical axis shows the characteristic root. FIG. 5 shows the analysis results of the hole drilling tools provided with cutting edges of different intervals. The horizontal axis of each chart shows the frequency and the vertical axis shows the characteristic root. FIG. 6 shows the relationship between the number of revolutions and the roundness obtained by carrying out the drilling with the drilling tools of Comparative Examples 1 and 2 and Examples 1 to 6 of the present invention. FIG. 7 shows the relationship between the number of revolutions and the roundness obtained by carrying out hole making with the hole making tools of Examples 7 to 12 of the present invention. FIG. 8 is a graph showing the relationship between the QCR value and the average roundness in Examples and Comparative Examples. FIG. 9 is a conceptual diagram showing the division angle of each cutting edge of the hole drilling tool. FIG. 10 is an explanatory view of mechanical terms of the hole drilling tool. FIG. 11 shows the relationship between the maximum real part σMAX of the quasi-static characteristic root and the average roundness. FIG. 12 shows the relationship between the characteristic root part and the number of rotations for Comparative Examples 1 and 2 and Examples 1 and 2. FIG. 13 shows the relationship between the maximum characteristic root and the number of polygons.

First, the Matsuzaki-Liu model will be described.
FIG. 1 is a drawing-substituting photograph showing a hole drilling tool (reamer) used for reaming.
In general reamer machining, the work material is fixed and machining is performed by rotating the reamer, but for the purpose of clarifying the basic characteristics, a simpler tool fixing and work material as an analysis model is used. The case of rotation will be handled. It is assumed that the work material has a prepared hole, and the center of the prepared hole and the axial center of the reamer coincide with each other in a normal cutting state where machining is performed without vibrating the tool.
FIG. 2 shows an analytical model of reaming in the case of 6 cutting edges. The figure shows the reamer as seen from the front of the cutting edge. The reamer does not rotate, and the work material rotates clockwise at an angular velocity ω. The reamer and the spindle are considered to move integrally, and only in-plane translational movement is considered, and rotational movement and bending and twisting of the reamer are ignored. Further, for simplicity, it is assumed that the reamer and the spindle are supported isotropically by the spring and the dashpot.
The coordinate system 0-xy fixed in the space with the center of the prepared hole as the origin is taken, and the coordinates of the center axis of the reamer are (x, y). The number of reamer blades is n, and one of the cutting edges is arranged in the positive direction of the x-axis. From this cutting edge, the cutting edge i (i = 1, 2, ..., N) is numbered in the direction opposite to the direction of rotation of the work material, and the angle of the cutting edge i from the x-axis is α _i . Note that α _i = 0 rad. It is considered that cutting force and contact force act on each cutting edge. It is assumed that cutting is performed only at the tip of the reamer in the axial direction, and the main component force of the cutting force and the back component force act on the cutting portion. In addition, in a portion other than the axial tip of the cutting edge, the normal force and frictional force due to contact with the processed hole are considered.

FIG. 3 shows the relationship between the cutting edge and the processed hole in the reaming in the case of 6 blades. In this figure, the surface of the machined hole is developed, and the horizontal axis represents the axial position and the vertical axis represents the circumferential angle. In this figure, the cutting edge is shown by a solid horizontal line, the left end of which represents the axial tip. The work material is fed while rotating with respect to the cutting edge.In the figure, the rotation is represented by the downward movement in the vertical direction, and the feed is represented by the movement in the right lateral direction. Move to the lower right along the diagonal direction. Therefore, cutting is performed at the most tip end portion in the axial direction of the cutting edge indicated by the red line, and in the subsequent portion, the cutting edge immediately before is in contact with the cut portion in order from the immediately preceding cutting edge.
Since cutting is performed on all cutting edges at the same time, the axial length cut by a certain cutting edge is the same as the length sent by the cutting edge of the immediately preceding cutting edge, as shown in Fig. 3. Become. Therefore, when the feed per one revolution of the work material is δ, the axial length δ _i of the portion cut by the cutting edge _i is as follows.

Here, δ is equal to the sum of the axial lengths of all the cutting edges. When the subscript j of α and δ exceeds n (j> n), it is defined by the following equation.

Here, in order to study the growth of minute vibrations of the reamer, assuming that the displacements x and y of the reamer are sufficiently smaller than the radius of the reamer, the radial displacement r _i of the cutting edge _i is approximately represented as follows.

The fluctuation P _i of the main component force of the cutting edge _i and the fluctuation Q _i of the back component force based on the state of normal cutting in which the center of the reamer does not move from the origin is the area of the portion cut by the cutting edge i. Assuming that it is proportional to the fluctuation amount of, the following equation holds.

Here, K _c represents the specific cutting resistance, and b represents the ratio of the back force component to the main force component.
Next, consider the contact force. It is assumed that the variation of the normal force with respect to the state of normal cutting can be modeled by a distributed spring and a distributed dashpot between the cutting edge and the work surface. The frictional force is assumed to be Coulomb frictional force. As shown in FIG. 3, if the numbers of l = 1, 2, ... Are sequentially given from the tip of the contact portion, the first contact portion of the cutting edge i is the time t− (α _{i + l)} by the cutting edge _{i + l.} It is a portion cut to −α _i ) / ω, and the axial length is δ _{i + 1} . The magnitude of the fluctuation of the contact force at each part is proportional to the difference between the radial displacement of the cutting edge and the amount of deformation of the hole surface in contact with the change over time, and the amount of deformation of the hole surface at the time when cutting was performed. Equal to the radial displacement of the cutting edge. Therefore, the change in normal force N _{i, j} and the change in frictional force F _{i, j at} the first contact portion of the cutting edge i are expressed by the following equations.

Here, k and c are the spring constant and the viscous damping coefficient per unit length between the cutting edge and the surface of the work material, and μ is the dynamic friction coefficient.
Assuming that the axial contact length between the cutting edge and the machined hole is δm, which corresponds to the feed for m rotations, the cutting edge contacts the machined hole in the range of l = 1, ..., N × m. In this case, the sum F _i of the variation of the sum N _i and the frictional force variation in normal force acting on the cutting edge i becomes the following equation.

Assuming that the equivalent masses of the reamer and the spindle are the equivalent spring constants in the M, x, and y directions and the equivalent viscous damping coefficients are K and C, respectively, the equation of motion of the reamer and the spindle is as follows.

Here, F _x and F _y are x and y direction components of fluctuations of forces (main component force, back force component, vertical drag force and frictional force) acting on the cutting edge, and are expressed as follows.

The solution of Equation 7 is assumed as follows.

Here, s represents a characteristic index made dimensionless by the rotational angular velocity ω. By substituting the equation 9 into the equation 7 and considering the equations 3 to 6 and the equation 8, the following equation is obtained.

Obtain the following characteristic equation from equation (10)

The results of analyzing the equation of motion of such a model are shown in the chart of FIG. 4 (equal division blade) and the chart of FIG. 5 (different division blade).

In the present invention, since the quasi-static characteristic root having the frequency ω = 0 is used, the characteristic equation of the Matsuzaki-Liu model can be summarized as follows.

The parameters (excluding the cutting edge arrangement angle (α _j )) used in analyzing the equation of motion are as follows.
Kcd / K = 1.0
kd / K = 1.0
b = 0.01
m = 0.10
m = 1
Here, m is an integer value and the others are dimensionless quantities.

Table 1 shows the results of analysis of the above equation of motion for each of the examples and comparative examples shown.

In Table 1, the maximum characteristic root shows the maximum value of the characteristic root (real part) in all frequencies and in the digonal to 13-sided polygon. Obtaining this value requires calculation of the amount of data required to draw many charts as shown in FIGS.
On the other hand, the maximum real part σ _MAX of the quasi-static characteristic root means that N ₀ is an integer value closest to the imaginary part of the quasi-static characteristic root s which is the characteristic root at the frequency ω = 0, and 3 ≦ N ₀ ≦ It indicates the largest real part of the quasi-static characteristic root s that satisfies 13.
The maximum real part σ _MAX of the quasi-static characteristic root s can be calculated (value on the vertical axis of each chart) only when the frequency ω = 0. Further, since the equation of motion is simplified at the frequency ω = 0, the burden on the calculation is greatly reduced. Therefore, many objects can be evaluated with the same load on the computer.
QCR value indicates the difference between the maximum real part Tishiguma _MAX of quasi-static characteristics roots up real Arushiguma _MAX and other examples and comparative examples of quasi-static characteristics roots of Comparative Example 1 (equally divided cutting edge).

Reaming tests were conducted on each of the examples and comparative examples so as to meet the analysis conditions. The basic test conditions were as follows (adjusted according to the type of material and reamer device).

About the reamer,
Diameter of groove bottom: φ5.2 mm
Groove depth: 1.4mm
Radius of groove roundness: R0.05-R0.3mm
Land width: Divided into different angles Margin width: 0.5 mm
Material: Cemented carbide hard coating material: TiN, TiAlN, TiSiN, AlCrN, etc. nitride hard coating target: Reamer all around

Workpiece <br/> Material: FC250 (gray iron casting)
Outer Diameter: φ8 (Outer Diameter of Reamer = 7.98)
Pilot hole diameter: φ7.5 (outer diameter of drill for pilot hole)
Length: prepared hole depth 26, reaming depth 24

Drilling conditions Rotation speed: 2000-6000 rpm
Progressive speed: Feed rate 200 to 600 mm / min Cutting speed (peripheral speed at φ8) 50 to 15 m / min
Cutting oil: Soluble type water-soluble cutting oil
Measuring conditions of inner diameter Measuring device: Taylron 365 manufactured by TAYLOR HOBSON
Measurement position: The reaming depth of 24 mm is 0.5 mm to 1 mm from the surface as the first surface, and the circularity of a total of 12 surfaces is measured at a pitch of 2 mm in the depth direction.

The test results of Examples and Comparative Examples are shown in FIGS. 6 and 7.
The vertical axis of each chart in FIGS. 6 and 7 indicates the circularity, and the horizontal axis indicates the rotation speed of the reamer.
The average roundness in Table 1 indicates the average roundness of each chart in FIGS. 6 and 7. In addition, the extremely roundness is excluded when calculating the average value. This is to remove an error due to the driving unit of the reamer device.

FIG. 8 shows the relationship between the QCR value in Table 1 and the average roundness. In Table 1, the two data on the right side show comparative examples, and the other data show examples.
It can be seen from FIG. 8 that the average roundness increases when the absolute value of the QCR value is 0.075 or more. Furthermore, its absolute value is preferably 0.10. More preferably, the absolute value is 0.125 or more.
In addition to the reamers of Comparative Examples 1 and 2 listed in Table 1, various reamers have been proposed and sold in the past. Some of them may accidentally have a QCR value exceeding each of the above thresholds. However, in evaluating the performance of the reamer, the QCR value proposed in this specification is a completely novel concept by the present inventors, and such an incidental conventional reamer does not disclose the concept at all. .. Therefore, even if such a reamer exists before the present application, it is considered that the present invention does not lose its novelty. And, if such a reamer exists before the application of the present application, it shall be excluded from the claims targeting the hole drilling tool.

From Table 1, the reamer having the angles and the cutting edges shown in each example show excellent characteristics (roundness). It is considered that even if the cutting edges are changed by ± 3 degrees depending on the angles of the cutting edges in each example, the same performance, that is, the reproducibility of the roundness can be obtained.
Particularly, the reamer having the cutting edge angular distribution shown in Examples 10 and 11 exhibits excellent characteristics (roundness).
It is considered that even if each cutting edge is changed by ± 5 degrees depending on the angle of the cutting edge, equivalent performance, that is, reproducibility of roundness can be obtained.
Therefore, another aspect of the present invention can be defined as follows. That is, it is a reamer with six cutting edges, and the arrangement angle of each cutting edge is 35 to 45 degrees, 75 to 85 degrees, 55 to 65 degrees, 50 to 60 degrees, 30 to 40 degrees, and 85 to 95 degrees. Is a reamer.
Furthermore, a reamer having 45 to 55 degrees, 25 to 35 degrees, 95 to 105 degrees, 65 to 75 degrees, 65 to 75 degrees, and 35 to 45 degrees in that order.

FIG. 9 schematically shows the disassembly angle of each cutting edge in the reamer. FIG. 10 schematically shows the cutting edge shape of the reamer.
When processing with a reamer, the larger the division angle, the greater the load applied to the cutting edge on the rear side in the rotation direction. This load accelerates the wear of the cutting edge. If there is a variation in the progress of wear in each cutting edge that constitutes the reamer, it becomes difficult to maintain a high roundness, and the durability is reduced.
Therefore, in order to prevent the occurrence of variation in wear of each cutting edge and to secure the rigidity of each cutting edge, the width of the cutting edge portion that contacts the work material (the width of the land portion (land width) or the margin portion) It is preferable to adjust the width (margin width) according to the spacing between the cutting edges (division angle).

More specifically, the size relationship when the dividing angle αi between the cutting edge i and the cutting edge i + 1 adjacent to the cutting edge i in the counter-rotational direction is viewed over the entire circumference of the processing tool, and the margin of the cutting edge i + 1 The size relationship when the width tmi + 1 and / or the land width ti + 1 is viewed in the entire circumferential direction of the processing tool is matched.
Furthermore, the ratio of the dividing angle when the dividing angle αi is seen all around the processing tool (α1: α2: ...: αn) and the ratio of the margin width when looking at the margin width all the way around the processing tool (tm2: tm3: ...: Tmn: tm1) and / or the land width ratio (t2: t3: ...: tn: tm1) when the land width is viewed over the entire circumference of the processing tool.

The results of other experiments conducted by the present inventors are shown in FIGS. 11 to 13.
FIG. 11 shows the relationship between the maximum real part σMAX of the quasi-static characteristic root and the average roundness. From this figure, it is understood that the maximum real part σMAX of the quasi-static characteristic root itself can also be an index showing the characteristic of the hole drilling tool.
Here, as compared with FIG. 8, it can be seen that the QCR value shows its characteristics more clearly.

Note that FIG. 12 shows the relationship between the characteristic root part of the characteristic equation of the Matsuzaki-Liu model and the rotation speed for Comparative Examples 1 and 2, and Examples 1 and 2.
FIG. 13 shows the relationship between the maximum characteristic root and the number of polygons.

The present invention is in no way limited to the description of each aspect and each embodiment. Various modifications are also included in the present invention within a range that can be easily conceived by a person skilled in the art without departing from the scope of claims.

Claims

A hole processing tool for forming a hole having a plurality of cutting edges,
When each cutting edge is applied to the equation of motion of the Matsuzaki-Liu model, the integer value closest to the imaginary part of the quasi-static characteristic root s, which is the characteristic root at the frequency ω = 0, is N 0 , and 3 ≦ N 0 ≦ 2n When the maximum real part of the quasi-static characteristic root s that satisfies +1 (n is the number of cutting edges) is the maximum real part σ MAX ,
Its maximum real part Tishiguma MAX the maximum real part Arushiguma MAX of the reference drilling tool is within the predetermined threshold, the drilling tool.
In the above equation of motion, quasi-static characteristic roots correspond to 2 to 13 polygons,
The reference hole processing tool is one in which the cutting edges are arranged at an equal pitch,
An absolute value of a difference between the maximum real part Tσ MAX of the target hole drilling tool and the maximum real part Rσ MAX of the reference hole drilling tool is 0.075 or more, provided that Tσ MAX ≤ Rσ MAX .
The hole drilling tool according to claim 2, wherein the absolute value of the difference is 0.10 or more.
The hole drilling tool according to claim 2, wherein the absolute value of the difference is 0.125 or more.
The hole drilling tool according to any one of claims 2 to 4, wherein the number of cutting edges n is 6.
The magnitude relationship when the dividing angle αi between the cutting edge i and the adjacent cutting edge i + 1 in the counter-rotating direction is viewed over the entire circumference of the hole making tool, and the margin width tmi + 1 of the cutting edge i + 1 or The processing tool according to any one of claims 2 to 5, wherein the land width ti + 1 is the same in size relationship when viewed in the entire circumferential direction of the hole processing tool.
Ratio of the division angle when the division angle αi is seen all around the hole drilling tool (α1: α2: ...: αn) and ratio of the margin width when the margin width is seen all around the hole drilling tool. (Tm2: tm3: ...: tmn: tm1) or the land width ratio (t2: t3: ...: tn: t1) when the land width is viewed over the entire circumference of the hole-machining portion is the same. The processing tool according to claim 6.
The processing tool according to claim 6 or 7, wherein a marginal portion of the cutting edge is covered with a hard film.
The processing tool according to any one of claims 1 to 8, wherein the hole processing tool is used for reaming.
A method of designing a hole drilling tool for forming a hole having a plurality of cutting edges,
An integer value closest to the imaginary part of the quasi-static characteristic root s, which is the characteristic root at the frequency ω = 0, is obtained by applying the plurality of cutting edges having an arbitrarily selected angle as the target processing tool to the characteristic equation of the Matsuzaki-Liu model. Identify N 0 ,
The maximum real part σ MAX that is the maximum real part of the quasi-static characteristic root s that satisfies 3 ≦ N 0 ≦ 2n + 1 (n is the number of cutting edges) is specified,
Its maximum real part Tishiguma MAX selects the target processing tool within a predetermined threshold range relative to the maximum real part Arushiguma MAX of the reference drilling tool, a method of designing a machined hole tool.
In the above characteristic equation, the quasi-static characteristic roots correspond to 2 to 13 polygons,
The reference hole processing tool is one in which the cutting edges are arranged at an equal pitch,
The absolute value of the difference between the maximum real part T σ MAX of the target hole drilling tool and the maximum real part R σ MAX of the reference hole drilling tool is 0.075, 0.10 or 0.125 or more, provided that T σ MAX The design method according to claim 10, wherein ≦ T σ MAX .
A method for manufacturing a hole making tool, which manufactures a hole making tool based on the design obtained by the designing method according to claim 10 or claim 11.
A method for evaluating a hole processing tool for forming a hole having a plurality of cutting edges,
By applying the plurality of cutting edges of the evaluation target processing tool to the characteristic equation of the Matsuzaki-Liu model, N 0 is specified as the integer value closest to the imaginary part of the quasi-static characteristic root s which is the characteristic root at the angular velocity ω = 0. Then
The maximum real part σ MAX of the maximum real part of the quasi-static characteristic root s that satisfies 3 ≦ N 0 ≦ 2n + 1 (n is the number of cutting edges) is specified,
Its maximum real part Tishiguma MAX the maximum real part Arushiguma MAX of the reference drilling tool is as acceptable the target processing tool within a predetermined threshold range, the evaluation method of the machined hole tool.
In the above characteristic equation, the quasi-static characteristic roots correspond to 2 to 13 polygons,
The reference hole processing tool is one in which the cutting edges are arranged at an equal pitch,
The absolute value of the difference between the maximum real part T σ MAX of the target hole drilling tool and the maximum real part R σ MAX of the reference hole drilling tool is 0.075, 0.10 or 0.125 or more, provided that T σ MAX The evaluation method according to claim 13, wherein ≦ Rσ MAX .
A method for evaluating a hole processing tool for forming a hole having a plurality of cutting edges,
The plurality of cutting edges of the processing tool to be evaluated are applied to the characteristic equation of the Matsuzaki-Liu model, and N 0 is specified as the integer value closest to the imaginary part of the quasi-static characteristic root s which is the characteristic root at angular velocity ω = 0. ,
An evaluation method in which the maximum real part σ MAX is specified as the maximum real part of the quasi-static characteristic root s that satisfies 3 ≦ N 0 ≦ 2n + 1 (n is the number of cutting edges).
Reamer with 6 cutting edges, and the arrangement angle of each cutting edge is 35 to 45 degrees, 75 to 85 degrees, 55 to 65 degrees, 50 to 60 degrees, 30 to 40 degrees, and 85 to 95 degrees. Reamer.
Reamer with 6 cutting edges, where the angle of each cutting edge is 45-55 degrees, 25-35 degrees, 95-105 degrees, 65-75 degrees, and 35-45 degrees.